Related papers: Bayesian and L1 Approaches to Sparse Unsupervised …

Dimension reduction algorithms aim to discover latent variables which describe underlying structures in high-dimensional data. Methods such as factor analysis and principal component analysis have the downside of not offering much…

We consider the prediction of weak effects in a multiple-output regression setup, when covariates are expected to explain a small amount, less than $\approx 1%$, of the variance of the target variables. To facilitate the prediction of the…

Deep learning models are known to often learn features that spuriously correlate with the class label during training but are irrelevant to the prediction task. Existing methods typically address this issue by annotating potential spurious…

Sparse regularization plays a central role in solving inverse problems arising from incomplete or corrupted measurements. Different regularizers correspond to different prior assumptions about the structure of the unknown signal, and…

Functional linear discriminant analysis offers a simple yet efficient method for classification, with the possibility of achieving a perfect classification. Several methods are proposed in the literature that mostly address the…

Sparse high-dimensional linear regression is a central problem in statistics, where the goal is often variable selection and/or coefficient estimation. We propose a mean-field variational Bayes approximation for sparse regression with…

Parameter estimates for associated genetic variants, report ed in the initial discovery samples, are often grossly inflated compared to the values observed in the follow-up replication samples. This type of bias is a consequence of the…

In this paper, we study the L1/L2 minimization on the gradient for imaging applications. Several recent works have demonstrated that L1/L2 is better than the L1 norm when approximating the L0 norm to promote sparsity. Consequently, we…

It has been shown both experimentally and theoretically that sparse signal recovery can be significantly improved given that part of the signal's support is known \emph{a priori}. In practice, however, such prior knowledge is usually…

In recent years, Bayesian statistics methods in neuroscience have been showing important advances. In particular, detection of brain signals for studying the complexity of the brain is an active area of research. Functional magnetic…

We consider Bayesian model selection in generalized linear models that are high-dimensional, with the number of covariates p being large relative to the sample size n, but sparse in that the number of active covariates is small compared to…

Efficiently quantifying predictive uncertainty in medical images remains a challenge. While Bayesian neural networks (BNN) offer predictive uncertainty, they require substantial computational resources to train. Although Bayesian…

$L_1$ regularized logistic regression has now become a workhorse of data mining and bioinformatics: it is widely used for many classification problems, particularly ones with many features. However, $L_1$ regularization typically selects…

We explore various Bayesian approaches to estimate partial Gaussian graphical models. Our hierarchical structures enable to deal with single-output as well as multiple-output linear regressions, in small or high dimension, enforcing either…

In this paper, we investigate the theoretical guarantees of penalized $\lun$ minimization (also called Basis Pursuit Denoising or Lasso) in terms of sparsity pattern recovery (support and sign consistency) from noisy measurements with…

Advances in sensing technology have made it possible to collect large volumes of high-dimensional time-series data. In fields like genetics and neuroscience, key questions concern whether directed relationships between variables can be…

Bayesian sparse factor models have proven useful for characterizing dependence in multivariate data, but scaling computation to large numbers of samples and dimensions is problematic. We propose expandable factor analysis for scalable…

We present a hierarchical Bayesian learning approach to infer jointly sparse parameter vectors from multiple measurement vectors. Our model uses separate conditionally Gaussian priors for each parameter vector and common gamma-distributed…

Two key challenges in modern statistical applications are the large amount of information recorded per individual, and that such data are often not collected all at once but in batches. These batch effects can be complex, causing…

We propose a generative model for robust tensor factorization in the presence of both missing data and outliers. The objective is to explicitly infer the underlying low-CP-rank tensor capturing the global information and a sparse tensor…